Phase Regularization and Additional Potential in Quantum Systems at the Potential Barrier to Maintain Adiabatic Condition

Authors

Anggen Dari , Iwan Setiawan , Andik Purwanto

DOI:

10.29303/jppipa.v10i2.6393

Published:

2024-02-28

Issue:

Vol. 10 No. 2 (2024): February

Keywords:

Additional Potential, Adiabatic, Fast Forward, Phase Regularization, Potential Barrier

Research Articles

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Dari, A., Setiawan, I. ., & Purwanto, A. . (2024). Phase Regularization and Additional Potential in Quantum Systems at the Potential Barrier to Maintain Adiabatic Condition. Jurnal Penelitian Pendidikan IPA, 10(2), 859–869. https://doi.org/10.29303/jppipa.v10i2.6393
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Abstract

This research is theoretical research with a literature study that examines methods to maintain characteristics of electrons when moving in a quantum system at the potential barrier. Attempts to maintain the characteristics of electrons in quantum systems are known as adiabatic. The method used in this research is the fast-forward method. This method was first introduced by Masuda and Nakamura in 2010. The fast-forward method is applied to barrier potential in case of electron energy larger and smaller than the potential barrier. This research focuses on preserving the characteristics of electrons by determining the regularization phase and additional potential of the quantum system at the barrier potential. The wave function solution of the system at the potential barrier is approximated by the Schrödinger equation into three regions for each case. The wave function of each region is regularized to be an adiabatic wave function and an additional term in the form of regularization phase (θ) is obtained. Given the regularized Hamiltonian, the additional potential (Ṽ) is obtained. The obtained regularization phase and additional potential ensure the quantum system at the potential barrier is in the same state from the initial state to the final state

References

Abah, O., & Lutz, E. (2018). Performance of Shortcut-to-Adiabaticity Quantum Engines. Physical Review E, 98(3), 032121. https://doi.org/10.1103/PhysRevE.98.032121

Agustin, N. C., Nugroho, C. I. W., & Pratama, M. A. (2019). Koefisien Transmisi Inn (Indium Nitrit) Penghalang Tunggal Hingga Penghalang Tiga dengan Metode Schrodinger. Fkip E-Proceeding, 4(1), 252–257.

Ainayah, N., Setiawan, I., & Hamdani, D. (2022). Methods to Accelerate Equilibrium in Overdamped Brownian Motion. Jurnal Pendidikan Fisika Dan Keilmuan (JPFK), 8(2), 1–11. https://doi.org/http://doi.org/10.25273/jpfk.v8i2.13626

Aini, N. R., Irianto, I. D., Hamid, A. A., & Thompson, B. B. (2020). Sejarah Perkembangan Fisika (Kuantum) dari Klasik hingga Modern. Diktat Kuliah Termodinamika, 4(3)(November), 22–32. https://doi.org/10.13140/RG.2.2.17085.08160

Babajanova, G., Matrasulov, J., & Nakamura, K. (2018). Quantum Gas in the Fast Forward Scheme of Adiabatically Expanding Cavities : Force and Equation of State. Physical Review E 97 , 042104, 042104, 1–10. https://doi.org/10.1103/PhysRevE.97.042104

Benggadinda, A., & Setiawan, I. (2021). Metoda Fast Forward Untuk Mempercepat Dinamika Kuantum Adiabatik Pada Spin Tunggal. JST (Jurnal Sains Dan Teknologi), 10(2), 274–280. https://doi.org/10.23887/jstundiksha.v10i2.39876

Born, M., & Fock, V. (1928). Beweis des Adiabatensatzes. Zeitschrift Fur Physik, 51(3–4), 165–180. https://doi.org/10.1007/BF01343193

Çakmak, B., & Müstecaplıoğlu, Ö. E. (2019). Spin Quantum Heat Engines with Shortcuts to Adiabaticity. Physical Review E, 99(3), 032108. https://doi.org/10.1103/PhysRevE.99.032108

Campo, A. del, Goold, J., & Paternostro, M. (2014). More Bang for Your Buck: Super-Adiabatic Quantum Engines. Scientific Reports, 4(1), 6208. https://doi.org/10.1038/srep06208

Chung, H.-C., Martínez-Garaot, S., Chen, X., Muga, J. G., & Tseng, S.-Y. (2019). Shortcuts to Adiabaticity in Optical Waveguides. EPL (Europhysics Letters), 127(3), 34001. https://doi.org/10.1209/0295-5075/127/34001

Deffner, S. (2016). Shortcuts to adiabaticity: Suppression of pair production in driven Dirac dynamics. New Journal of Physics, 18(1). https://doi.org/10.1088/1367-2630/18/1/012001

Dupays, L., Egusquiza, I. L., del Campo, A., & Chenu, A. (2020). Superadiabatic Thermalization of A Quantum Oscillator by Engineered Dephasing. Physical Review Research, 2(3), 033178. https://doi.org/10.1103/PhysRevResearch.2.033178

Elisa, N., Setiawan, I., & Hamdani, D. (2023). Energi Penggerak untuk Mempercepat Kesetimbangan Gerak Brown Teredam Sebagian (Underdamped). Jurnal Inovasi Dan Pembelajaran Fisika, 10(1), 21–33. https://doi.org/10.36706/jipf.v10i1.19240

Elviyanti, I. L., Pratiwi, B. N., & Syukron, A. (2023). Pendekatan Semiklasik untuk Persamaan Schrodinger dengan Potensial Scraf II Trigonometri. Delta Journal of Physics, 1(1), 32–38.

Guéry-Odelin, D., Ruschhaupt, A., Kiely, A., Torrontegui, E., Martínez-Garaot, S., & Muga, J. G. (2019). Shortcuts to Adiabaticity: Concepts, Methods, and Applications. Reviews of Modern Physics, 91(4), 045001. https://doi.org/10.1103/RevModPhys.91.045001

Hartmann, A., Mukherjee, V., Niedenzu, W., & Lechner, W. (2020). Many-Body Quantum Heat Engines with Shortcuts to Adiabaticity. Physical Review Research, 2(2), 23145. https://doi.org/10.1103/PhysRevResearch.2.023145

Hutagalung, M., Setiawan, I., & Hamdani, D. (2023). Kajian Literatur Fase Adiabatik untuk mempercepat Dinamika Kuantum Adiabatik pada Osilator Harmonik. Indonesian Journal of Applied Physics, 13(1), 106. https://doi.org/10.13057/ijap.v12i2.65252

Jarzynski, C., Deffner, S., Patra, A., & Subaşl, Y. (2017). Fast Forward to the Classical Adiabatic Invariant. Physical Review E, 95(3), 1–7. https://doi.org/10.1103/PhysRevE.95.032122

Khujakulov, A., & Nakamura, K. (2016). Scheme for Accelerating Quantum Tunneling Dynamics. Physical Review A, 93(2), 1–14. https://doi.org/10.1103/PhysRevA.93.022101

Kiely, A., McGuinness, J. P. L., Muga, J. G., & Ruschhaupt, A. (2015). Fast and Stable Manipulation of A Charged Particle in a Penning Trap. Journal of Physics B: Atomic, Molecular and Optical Physics, 48(7). https://doi.org/10.1088/0953-4075/48/7/075503

Liu, X.-C., & Kong, X.-Y. (2023). Quantum Simulation of the Shortcut to the Adiabatic Passage Using Nuclear Magnetic Resonance. Entropy, 25(7), 1020. https://doi.org/10.3390/e25071020

Masuda, S., & Nakamura, K. (2010). Fast-Forward of Adiabatic Dynamics in Quantum Mechanics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2116), 1135–1154. https://doi.org/10.1098/rspa.2009.0446

Masuda, S., & Nakamura, K. (2022). Fast-Forward Scaling Theory. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380(2239). https://doi.org/10.1098/rsta.2021.0278

Nakamura, K., Khujakulov, A., Avazbaev, S., & Masuda, S. (2017). Fast forward of Adiabatic Control of Tunneling States. Physical Review A, 95(6), 062108. https://doi.org/10.1103/PhysRevA.95.062108

Nakamura, K., Matrasulov, J., & Izumida, Y. (2020). Fast-Forward Approach to Stochastic Heat Engine. Physical Review E, 102(1), 1–12. https://doi.org/10.1103/PhysRevE.102.012129

Patra, A., & Jarzynski, C. (2021). Semiclassical Fast-Forward Shortcuts to Adiabaticity. Physical Review Research, 3(1). https://doi.org/10.1103/PhysRevResearch.3.013087

Romadani, A., & Rani, E. (2020). Solusi Persamaan Dirac untuk Fermion dengan Model Potensial Penghalang Medan Elektromagnetik. Jurnal Fisika Flux: Jurnal Ilmiah Fisika FMIPA Universitas Lambung Mangkurat, 17(2), 112. https://doi.org/10.20527/flux.v17i2.8105

Santos, A. C., & Sarandy, M. S. (2018). Generalized Shortcuts to Adiabaticity and Enhanced Robustness Against Decoherence. Journal of Physics A: Mathematical and Theoretical, 51(2), 025301. https://doi.org/10.1088/1751-8121/aa96f1

Setiawan, I. (2019). Dinamika Spin Kuantum Adiabatik Dipercepat pada Model Landau-Zener dan Model Ising. Jurnal Kumparan Fisika, 2(1), 57–64. https://doi.org/10.33369/jkf.2.1.57-64

Setiawan, I., Eka Gunara, B., Masuda, S., & Nakamura, K. (2017). Fast forward of the Adiabatic Spin Dynamics of Entangled States. Physical Review A, 96(5), 1–11. https://doi.org/10.1103/PhysRevA.96.052106

Setiawan, I., Ekawita, R., Sugihakim, R., & Gunara, B. E. (2023). Fast-Forward Adiabatic Quantum Dynamics of XY Spin Model on Three Spin System. Physica Scripta, 98(2), 025405. https://doi.org/10.1088/1402-4896/acb2fe

Setiawan, I., Gunara, B. E., Avazbaev, S., & Nakamura, K. (2019). Fast-forward Approach to Adiabatic Quantum Dynamics of Regular Spin Clusters: Nature of Geometry-Dependent Driving Interactions. Physical Review A, 99(6), 062116. https://doi.org/10.1103/PhysRevA.99.062116

Setiawan, I., Gunara, B. E., & Nakamura, K. (2019). Fast forward of Adiabatic Spin Dynamics : An Application to Quantum Annealing Model in Triangle Spin Systems. Journal of Physics: Conference Series, 1245(1). https://doi.org/10.1088/1742-6596/1245/1/012077

Setiawan, I., Sugihakim, R., Gunara, B. E., Masuda, S., & Nakamura, K. (2023). Fast-Forward Generation of Non-Equilibrium Steady States of a Charged Particle Under the Magnetic Field. Progress of Theoretical and Experimental Physics, 2023(6), 1–12. https://doi.org/10.1093/ptep/ptad067

Setiawan, I., Syarkowi, A., Syatyatuhu, A., & Gunara, B. E. (2021). Driving Energy to Accelerate the Adiabatic Electron Dynamics in Quantum Hall System Driving Energy to Accelerate the Adiabatic Electron Dynamics in Quantum Hall System. Journal of Physics: Conference Series, 1731(1). https://doi.org/10.1088/1742-6596/1731/1/012065

Steckmann, T., Keen, T., Kökcü, E., Kemper, A. F., Dumitrescu, E. F., & Wang, Y. (2023). Mapping the metal-insulator phase diagram by algebraically fast-forwarding dynamics on a cloud quantum computer. Physical Review Research, 5(2), 1–16. https://doi.org/10.1103/PhysRevResearch.5.023198

Sudiarta, I. W. (2019). Mekanika Kuantum. Mataram: CV. Garuda Ilmu

Sugihakim, R., Setiawan, I., & Gunara, B. E. (2021). Fast-Forward of Local-Phased-Regularized Spinor in Massless 2+1-Dimensions Adiabatic Dirac Dynamics. Journal of Physics: Conference Series, 1951(1). https://doi.org/10.1088/1742-6596/1951/1/012068

Taras, A. K., Tuniz, A., Bajwa, M. A., Ng, V., Dawes, J. M., Poulton, C. G., & De Sterke, C. M. (2021). Shortcuts to Adiabaticity in Waveguide Couplers–Theory and Implementation. Advances in Physics: X, 6(1). https://doi.org/10.1080/23746149.2021.1894978

Villazon, T., Polkovnikov, A., & Chandran, A. (2019). Swift Heat Transfer by Fast-Forward Driving in Open Quantum Systems. Physical Review A, 012126(July), 1–15. https://doi.org/10.1103/PhysRevA.100.012126

Wardani, I., Aisyah, N. D., & Supardi, A. (2020). Approximation Rectangular Function as Potential Barrier. Journal of Physics: Conference Series, 1445(1). https://doi.org/10.1088/1742-6596/1445/1/012009

Wen, Z., & Wu, D. (2020). Ferroelectric Tunnel Junctions: Modulations on the Potential Barrier. Advanced Materials, 32(27), 1–19. https://doi.org/10.1002/adma.201904123

Yu, X., Zhang, Q., Ban, Y., & Chen, X. (2018). Fast and Robust Control of Two Interacting Spins. Physical Review A, 97(6), 062317. https://doi.org/10.1103/PhysRevA.97.062317

Zettili, N. (2009). Quantum Mechanics: Theory, Analysis, and Applications (2nd ed.). Jacksonville State University, USA: WILEY.

Author Biographies

Anggen Dari, Universitas Bengkulu

Iwan Setiawan, University of Bengkulu

Andik Purwanto, University of Bengkulu

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